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T. Schnitzer

Bio: T. Schnitzer is an academic researcher from University of Freiburg. The author has contributed to research in topics: Conservation law & Finite volume method. The author has an hindex of 2, co-authored 2 publications receiving 1057 citations.

Papers
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Journal ArticleDOI
TL;DR: A new approach to the stabilization of numerical schemes in magnetohydrodynamic processes in which the divergence errors are transported to the domain boundaries with the maximal admissible speed and are damped at the same time is developed.

1,194 citations

Book ChapterDOI
01 Jan 2003
TL;DR: Numerical experiments for hyperbolic conservation laws in multiple space dimensions are presented to compare their efficiency for different situations, including the Euler equations of gas dynamics and Lundquist's equations of ideal magneto-hydrodynamics (MHD).
Abstract: The methods most frequently used in computational fluid mechanics for solving the compressible Navier-Stokes or compressible Euler equations are finite volume schemes on structured or on unstructured grids. First order as well as higher order space discretizations of MUSCL type, including flux limiters and higher order Runge- Kutta methods for the time discretization, guarantee robust and accurate schemes. But there is an important difficulty. If one increases the order, the stencil for the space discretization increases too, and the scheme becomes very expensive. Therefore schemes with more compact stencils are necessary. Discontinuous Galerkin schemes in the sense of [3] are of this type. They are identical to finite volume schemes in the case of formal first order, and for higher order they use nonconformal ansatz functions whose restrictions to single cells are polynomials of higher order. Therefore they seem to be more efficient and it is of highest interest to compare finite volume and discontinuous Galerkin methods for real applications with respect to their efficiency. Experiences [1] with the Euler equations of gas dynamics indicate that the discontinuous Galerkin methods have some advantages. Since there are no systematic studies available in the literature, we will present in this paper some numerical experiments for hyperbolic conservation laws in multiple space dimensions to compare their efficiency for different situations. As important instances of hyperbolic conservation laws we consider the Euler equations of gas dynamics and Lundquist’s equations of ideal magneto-hydrodynamics (MHD). Furthermore we have found a new limiter which improves the results from [14]. Similar studies have been done in [4].

4 citations

Journal ArticleDOI
20 Apr 2022-Pain
TL;DR: PAIN as mentioned in this paper is a journal for the dissemination of research in the basic and clinical sciences of multidisciplinary interest, focusing on the nature, mechanisms and treatment of pain in humans.
Abstract: PAIN publishes research on the nature, mechanisms and treatment of pain. The journal provides a forum for the dissemination of research in the basic and clinical sciences of multidisciplinary interest.

3 citations


Cited by
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Journal ArticleDOI
TL;DR: Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods.
Abstract: A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has been designed to be easily extensible for use with static and adaptive mesh refinement. It combines higher order Godunov methods with the constrained transport (CT) technique to enforce the divergence-free constraint on the magnetic field. Discretization is based on cell-centered volume averages for mass, momentum, and energy, and face-centered area averages for the magnetic field. Novel features of the algorithm include (1) a consistent framework for computing the time- and edge-averaged electric fields used by CT to evolve the magnetic field from the time- and area-averaged Godunov fluxes, (2) the extension to MHD of spatial reconstruction schemes that involve a dimensionally split time advance, and (3) the extension to MHD of two different dimensionally unsplit integration methods. Implementation of the algorithm in both C and FORTRAN95 is detailed, including strategies for parallelization using domain decomposition. Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods. The source code is freely available for download on the web.

1,096 citations

Journal ArticleDOI
TL;DR: The framework and the adaptive algorithms enable physics-based space weather modeling and even short-term forecasting and the algorithms of BATL, the Block-Adaptive Tree Library, are described and its efficiency and scaling properties for various problems are described.

693 citations

Journal ArticleDOI
TL;DR: In this paper, a multi-state Harten-Lax-van Leer (HLL) approximate Riemann solver for the ideal magnetohydrodynamic (MHD) equations is developed based on the assumption that the normal velocity is constant over the riemann fan.

668 citations

Journal ArticleDOI
TL;DR: A basic grounding in the fundamentals of SPH is given, showing how the equations of motion and energy can be self-consistently derived from the density estimate, and how to interpret these equations using the basic SPH interpolation formulae is shown.

611 citations

Journal ArticleDOI
TL;DR: A conservative least-squares polynomial reconstruction operator is applied to the discontinuous Galerkin method, which yields space–time polynomials for the vector of conserved variables and for the physical fluxes and source terms that can be used in a natural way to construct very efficient fully-discrete and quadrature-free one-step schemes.

555 citations